Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 18

Chapter 3, Problem 18

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-1/4, -1/7) and (3/4, 6/7)

Verified step by step guidance

Identify the coordinates of the two points: \(\left(-\frac{1}{4}, -\frac{1}{7}\right)\) and \(\left(\frac{3}{4}, \frac{6}{7}\right)\).

Recall the distance formula between two points \(\left(x_1, y_1\right)\) and \(\left(x_2, y_2\right)\): \[d = \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2}\]

Calculate the difference in the \(x\)-coordinates: \[x_2 - x_1 = \frac{3}{4} - \left(-\frac{1}{4}\right) = \frac{3}{4} + \frac{1}{4}\]

Calculate the difference in the \(y\)-coordinates: \[y_2 - y_1 = \frac{6}{7} - \left(-\frac{1}{7}\right) = \frac{6}{7} + \frac{1}{7}\]

Substitute these differences into the distance formula, simplify the expression under the square root to get the simplified radical form, and then approximate the decimal value rounded to two decimal places.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distance Formula

The distance formula calculates the length between two points in a coordinate plane. It is derived from the Pythagorean theorem and given by √[(x2 - x1)² + (y2 - y1)²]. This formula helps find the straight-line distance between points with coordinates (x1, y1) and (x2, y2).

Simplifying Radical Expressions

Simplifying radicals involves reducing the square root expressions to their simplest form by factoring out perfect squares. This process makes the answer more exact and easier to interpret before rounding. For example, √50 can be simplified to 5√2.

Rounding Decimal Numbers

Rounding is the process of approximating a number to a specified number of decimal places for clarity and practicality. After calculating the exact distance, rounding to two decimal places provides a concise and usable numerical answer, such as 1.23 instead of 1.23456.

Recommended video:

4:47

The Number e

Related Practice

Textbook Question

In Exercises 11–26, determine whether each equation defines y as a function of x. 4x = y²

views

Textbook Question

Use the graph to determine (a) the function's domain, (b) the function's range, (c) the x-intercepts, if any, (d) the y-intercept, if there is one, (e) intervals on which the function is increasing, decreasing or constant, (f) the missing function values, indicated by question marks, below each graph.

440

views

Textbook Question

Find the domain of each function. f(x) = √(x - 3)

1300

views

Textbook Question

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−1, 5) and is perpendicular to the line whose equation is x = 6.

123

views

Textbook Question

Find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)

869

views

Textbook Question

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (7/3, 1/5) and (1/3, 6/5)

898

views